相关论文: Selberg Type Integrals Associated with $sl_3$
The aim of this work is to generalize a very important type of Lie algebras and superalgebras, i.e. filiform Lie (super)algebras, into the theory of Lie algebras of order F$. Thus, the concept of filiform Lie algebras of order F is…
This paper gives a fairly explicit formula for the Hilbert series of algebras of Veronese type.
Two types of higher order Lie $\ell$-ple systems are introduced in this paper. They are defined by brackets with $\ell > 3$ arguments satisfying certain conditions, and generalize the well known Lie triple systems. One of the…
A series invariant for a certain class of closed 3-manifolds associated with a type I Lie superalgebra sl(m|n) was introduced recently. We find a q-series for the other Lie superalgebra of the same type of the minimum rank.
We study and classify kinematical algebras which appear in the framework of Lie superalgebras or Lie algebras of order three. All these algebras are related through generalised Inon\"u-Wigner contractions from either the orthosymplectic…
The three-algebras used by Bagger and Lambert in N=6 theories of ABJM type are in one-to-one correspondence with a certain type of Lie superalgebras. We show that the description of three-algebras as generalized Jordan triple systems…
We classify blocks in the BGG category $\mathcal O$ of modules of non-integral weights for the exceptional Lie superalgebra $G(3)$. We compute the characters for tilting modules of non-integral weights in $\mathcal O$. Reduction methods are…
We prove some isomorphisms between exceptional W-algebras associated with exceptional simple Lie algebras.
In this paper we initiate a general classification for Lie algebras of order 3 and we give all Lie algebras of order 3 based on $\mathfrak{sl}(2,\mathbb C)$ and $\mathfrak{iso}(1,3)$ the Poincar\'e algebra in four-dimensions. We then set…
We illustrate some simple ideas that can be used for obtaining a classification of small-dimensional solvable Lie algebras.Using these we obtain the classification of 3 and 4 dimensional solvable Lie algebras (over fields of any…
We prove a reciprocity formula that relates a spectral average of products of triple product integrals involving automorphic forms of weights $0$ and $1/2$ to the classical Rankin-Selberg integrals for automorphic forms of weight $0$.
The index of a Lie algebra is an important invariant which arises in several areas, e.g. in the study of coadjoint orbits for a Lie group, in invariant theory and in representation theory. We study the index for several classes of nilpotent…
The PostLie algebra is an enriched structure of the Lie algebra that has recently arisen from operadic study. It is closely related to pre-Lie algebra, Rota-Baxter algebra, dendriform trialgebra, modified classical Yang-Baxter equations and…
We establish combinatorial formulas for the index of a class of matrix Lie algebras whose matrix forms are encoded by strict partial orderings.
All solvable Lie algebras with Heisenberg nilradical have already been classified. We extend this result to a classification of solvable Leibniz algebras with Heisenberg nilradical. As an example, we show the complete classification of all…
Algorithms for numerical computation of symmetric elliptic integrals of all three kinds are improved in several ways and extended to complex values of the variables (with some restrictions in the case of the integral of the third kind).…
We develop a theory of toroidal vertex algebras and their modules, and we give a conceptual construction of toroidal vertex algebras and their modules. As an application, we associate toroidal vertex algebras and their modules to toroidal…
We introduce the concept of 3-Lie-Rinehart superalgebra and systematically describe a cohomology complex by considering coefficient modules. Furthermore, we study the relationships between a Lie-Rinehart superalgebra and its induced…
We provide the explicit formula for orbital integrals associated with elliptic regular semisimple elements in $\mathrm{GL}_n(F) \cap \mathrm{M}_n(\mathfrak{o})$ and associated with arbitrary elements of the spherical Hecke algebra of…
We give an explicit formula for the Hilbert Series of an algebra defined by a linearly presented, standard graded, residual intersection of a grade three Gorenstein ideal.